Abstract
The statistical mechanics of an isolated self-gravitating system consisting ofN uniform mass sheets is considered using both canonical and microcanonical ensembles. The one-particle distribution function is found in closed form. The limit for large numbers of sheets with fixed total mass and energy is taken and is shown to yield the isothermal solution of the Vlasov equation. The order of magnitude of the approach to Vlasov theory is found to be 0(1/N). Numerical results for spatial density and velocity distributions are given.
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Rybicki, G.B. Exact statistical mechanics of a one-dimensional self-gravitating system. Astrophys Space Sci 14, 56–72 (1971). https://doi.org/10.1007/BF00649195
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DOI: https://doi.org/10.1007/BF00649195